On a transmission boundary-value problem for the time-harmonic Maxwell equations without displacement currents

This paper considers a transmission boundary-value problem for the time-harmonic Maxwell equations neglecting displacement currents. The usual transmission conditions, which require the continuity of the tangential components of the electric and magnetic fields across boundaries, are slightly modified. For this new problem, it is shown that the uniqueness of the solution depends on the topological properties of the domains under consideration. Finally, existence results are obtained by using a boundary integral equation approach.